ringearV

2021-02-11

For $y=\text{}-{\mathrm{log}}_{2}x$ .

a) Use transformations of the graphs of$y={\mathrm{log}}_{2}x$ and $y={\mathrm{log}}_{3}x$ o graph the given functions.

b) Write the domain and range in interval notation.

c) Write an equation of the asymptote.

a) Use transformations of the graphs of

b) Write the domain and range in interval notation.

c) Write an equation of the asymptote.

davonliefI

Skilled2021-02-12Added 79 answers

Step 1

a) Start from the graph of the parent function$f\left(x\right)={\mathrm{log}}_{2}x$ .

As we can see the given function$y=\text{}-{\mathrm{log}}_{2}x$ can be expressed in terms of the parent function f as $y=\text{}-f\left(x\right)$

This indicates that the graph of the function$y=\text{}-{\mathrm{log}}_{2}x$ will be the same as the graph of the parent function $f\left(x\right)={\mathrm{log}}_{2}x$ reflected through the x-axis.

See the graphs in the picture below:

Step 2

b) The domain of the function$y=\text{}-{\mathrm{log}}_{2}x$ is the interval: $(0,\text{}+\mathrm{\infty})$

The range of the function$y=\text{}-{\mathrm{log}}_{2}x$ is the interval $(-\mathrm{\infty},\text{}+\mathrm{\infty})$

c) The vertical asymptote of the graph of this function is the line$x=0$

a) Start from the graph of the parent function

As we can see the given function

This indicates that the graph of the function

See the graphs in the picture below:

Step 2

b) The domain of the function

The range of the function

c) The vertical asymptote of the graph of this function is the line